IXL | Perimeter and area: changes in scale

Look at this rectangle:

9 mm

10 mm

If both dimensions are doubled, then which of the following statements about its perimeter will be true?

The new perimeter will be

times the old perimeter.

The new perimeter will be

of the old perimeter.

The new perimeter will be

times the old perimeter.

The new perimeter will be

times the old perimeter.

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Learn with an example

question

Look at this square:

7 ft

If the side lengths are tripled, then which of the following statements about its perimeter will be true?

The new perimeter will be

times the old perimeter.

The new perimeter will be

of the old perimeter.

The new perimeter will be

times the old perimeter.

The new perimeter will be

times the old perimeter.

solution

You can solve this problem without using the measurements given in the diagram.

The original square had this perimeter:

P = 4s

The new square will have sides that are 3 times as long. Since the original side lengths were s, the new side lengths will be 3s. Calculate the perimeter:

P	=	4(3s)

	=	12s

Divide the new perimeter by the original perimeter and simplify.

new perimeter

original perimeter

12s

The new perimeter will be

times the old perimeter.

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Teacher tools

Work it out

Not feeling ready yet? These can help:

GG.6Area of triangles

GG.4Area of parallelograms

GG.2Area of rectangles and squares

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